the vagaries at least of that empiricism which doubts all rational perception. Thus has mathematics proved the foundation of the speculation of philosophers of divergent views and in different environments. Its connection with theology, as found in Plato, Pythagoras, and the medieval teachers, is not so artificial as it might seem to many to-day.'

6. Mathematics thus affords the most varied preparation for the higher sciences. Still it does not of itself furnish the motives to go beyond its own field and to take up the higher sciences. On the contrary (and here we have an opportunity to note the harmful effects of a one-sided study of this branch) it is a charge frequently made against mathematics that it fills its devotees with self-satisfaction and contempt for all other sciences and their methods a state of mind that is evidently irreconcilable with the scientific spirit. A one-sided pursuit of this science is undoubtedly harmful and may be the death of noble mental organs. Mathematics provides little food for the imagination or the feelings; only indirectly and under wise guidance will it meet the ideal tendency of the soul. Goethe is severe in his arraignment of its defects: "Mathematics can not clear the mind of one single prejudice; it can not cure stubbornness; it can not infuse a broadly human spirit; it is simply incapable of exercising any moral influence." But what he says is true only of what mathematics can do directly and of itself. Leibnitz finds fault with the false methods followed in his day in the study of mathematics, and says that this abuse had brought it about that "the study of antiquity and all solid research were a matter almost of contempt." Descartes says of the extreme mathematicians, "There is no more vacuous occupation than to busy oneself so much with numbers and imaginary figures, as though these trifles were the be-all and end-all of studies, and to waste so much energy on superfluous proofs, as though one would deprive himself, in a measure, of the use of reason."

Mathematics is after all but one of the educational elements, and at that, neither the highest nor the most indispensable. It must needs be supplemented by philology, philosophy, and religious instruction, and must be correlated with the other branches of the curriculum-a subject that has as yet received but scant attention.

1 Vol. I, ch. XVI, 2.

2 For the references see Dupanloup, L'Education, t. I, liv. 4, chap. 2, where these viewpoints are developed more fully.

CHAPTER XXIV.

Philosophy.

1. The educative process, if deep and serious, will be confronted at many points with the problems of philosophy. The eye of the mind is at first attracted by the variety of things and the diversity of the phenomena. But once it has grown sharper, it will try to penetrate into their interrelations: the eye will pass from the facts back to their causes; it will discern the necessary behind the accidental, and the rational behind the arbitrary. This is the transition from the empirical interest to the speculative, and the progress from the searching after knowledge to the searching after causes.' This tendency of the mind contains one of the forces that have created philosophy, and, though men may declare philosophy dead, yet this tendency will never die out and it is strong enough to recall philosophy again and again to a new and vigorous life.

A further impetus to philosophize is the tendency to reflect on life. Here the mind passes from the perception of a thing to the judgment of it. What it seeks is not so much an explanation as enlightenment. It is less concerned with the linking of causes than with the grading of values. This tendency is the direct result of the wide-awake mental life and the independent thinking that characterize education." The ability to profit, not merely by our own experience, but also by that of 'others, to render an account of one's views and actions, to set up a standard for judging the views and actions of others, to illumine our daily life with thought, and to vitalize what we have thought by bringing it into contact with our past experiencethe ability to do all this denotes a high degree of education and shows how the latter is akin to wisdom. This high point will not be reached except by one who is of a mature mind, who has spontaneously begun to reflect and judge, who has individually felt certain interests, and who has associated with the world and But the reflection which has been thus inaugurated must be guided by well-established principles, so that the various observations can be connected and harmonized with one another. We may not be satisfied with mere philosophizing; but philoso

men.

phy itself must be allowed to furnish, one may say, the trelliswork for supporting the vines of the individual reflections; the individual thinking must ever remain in touch with the treasures unearthed by the world's great thinkers.

If conducted far enough, the speculative interest and the interest in enlightenment will meet in the search after a view of the world and of life (Welt- und Lebensanschauung). This view will extend its horizon as far as possible; science and art, poetry and reality, the present and the past, nature and history-all these the view of the world and of life will lay under contribution for materials to substantiate its claims. But the elaboration of these materials must be left to philosophy, and the latter can here give a good account of its universality as well as distinguish the ephemeral from the solid and permanent. Philosophy shows how the creative thinkers have conceived the different problems, and what progress they have made in their solution. Recalling the connection between the physical and the moral, philosophy projects the world-view into the life of the individual and demonstrates how the opinions strive to be verified by the maxims, how the conception of life seeks a counterpart and substantiation in the actual living. On account of this contribution to education philosophy is a strong element making for enlightenment and is ultimately a moral force.

2. The direct contributions of philosophy to the educative process are the following: deepening of the speculative interest, mental enlightenment, and a world-view. All three elements may be seen distinctly separate in time and duly graduated in the early and later periods of Greek philosophy. The pre-Sophists represent a speculation that is still experimental and tentative, though increasing in depth. The Sophists and Socrates are engaged in the work of enlightenment and are striking examples of the right and the wrong methods that may be pursued in this regard. Finally, Plato and Aristotle offer harmonious, unified, and complete views of the world and life, and their views are alike distinguished for their broad outlook and their moral depth. Plato comprised in his system all previous speculation. But Aristotle applied philosophy to the individual sciences, thus laying the foundation for the great influence that philosophy was ever after to exert on all the sciences and, therefore, indirectly on education also. Aristotle made logic the organon of science. He connected philosophy with literature when he treated poetics. and rhetoric philosophically. In the department of natural philosophy he inaugurated the various descriptive disciplines.

Political economy he supplemented by constitutional history. In his speculative theology he furnished the Christian thinkers. with the material for differentiating natural and supernatural theology.

The individual sciences have, in the course of their subsequent development, grown to be more and more independent, but it remains the function of philosophy to show their interrelation. As the science of principles, philosophy represents the unity of science in general; and within the domain of the individual sciences it is only through philosophy that any subject can be viewed from a broad and general viewpoint. Plato says, "He who is capable of surveying the whole is capable also of speculation;" and the converse of this is also true: "The speculative conception makes us capable of surveying the whole. Philosophy deepens and clarifies the sciences. It assists them in formulating their problems and in delimiting their fields of inquiry. It co-operates with them in developing their methods, and supplies their systematic structure. Philosophical training is hence a preparatory training for science, and the elements. of philosophy are an essential part of a course of instruction. that is to fit the pupil for the pursuit of science.

3. The school subjects themselves converge into the philosophical instruction, and this is a convincing proof that philosophy is essential to higher education. The language instruction trains the pupils in the use of concepts in so far as these are expressed in words, and logic teaches the use of concepts as such. In language instruction the concepts are treated as language elements, and in logic they are regarded as thought contents: but the two views belong together. Thought embodied in language disciplines the mind; but the choicest fruit of this discipline is obtained only after the mind studies in logic its own operations. Literature represents the results of intellectual, æsthetical, and moral activities; the explanation of the text is only the beginning of the analysis, and the further steps must be guided by psychological, æsthetical, and ethical principles. The moral gains to be obtained from literature and history depend, to a great extent, upon whether the moral reflections to which these subjects give rise are developed far enough to consolidate. But to do this, the teacher must be at home in practical philosophy, and the pupil must likewise have some guiding principles that he may apply to moral materials. High-flying, ethical and æsthetical disquisitions are, indeed, of little value.

But neither will moral remarks, if merely incidental and incoherent, raise the educative value of a subject to any appreciable degree. What is needed are fixed and clear-cut principles that are part and parcel of a complete system of philosophy; and these must be presented as such and not as the outcome of haphazard reflection.1

Mathematics, the school of exact thinking, is consequently the preparatory school for scientific logic. Though it is unequalled for the obtaining of rational perceptions that lie within its own domain, still its scope is confined to this domain, the field of quantities. Once this limitation is understood, mathematics will serve as a guide to the general domain of rational perception.

A deep interest in speculation may, admittedly, be enkindled even in early life by mathematics; but the test of the elastic force of this interest is after all the progress from the understanding of the relations of quantity to the understanding of the fundamental relations of things. Natural science also awakens a strong speculative interest; but it, too, must be supplemented in this by philosophical instruction. Allow philosophy its proper place in the curriculum, and the natural science instruction will be less prone to treat its materials too extensively, as is frequently, done to the loss of much of the educative content of this subject. Philosophy joins the physical and ethical elements of the course of study and may thus be instrumental in uniting the sciences and the classics, the realia and the humanities, whose antagonism is the greatest menace to the unity of our higher education.

The theological element of instruction must also be supplemented by the philosophical, for the two subjects are intimately connected. Theology grew strong first by opposing philosophy and then by allaying itself with its former enemy, and now theology and philosophy are joined in a friendly union in the works of Christian thinkers: dogmatics has adopted many definitions of metaphysics, and moral theology has enriched itself with the spoils of ancient ethics and has in turn supplied the basis for a deeper philosophical ethics. No apology of Christi

'Herbart calls the system of philosophy the keystone of instruction: “To completely teach how life is determined by its two rulers, Speculation and Taste, we must search for a system of philosophy, the keystone of instruction." (The Science of Education, Transl. by Henry M. and Emmie Felkin, London, 1892, p. 195.)